Optical Communication Network
Latency is a major issue in high speed communication networks, such as optical networks. This makes the trade-off between latency, complexity of implementation and coding gain important in the selection of channel codes. In many cases, the use of any coding technique can only provide gain at the expense of additional decoding and encoding complexity and increased latency. It is important to find coding techniques that provide sufficient gains, while keeping the encoding and decoding complexity low.
Reed-Muller (RM) Codes
Polar codes, see U.S. Pat. No. 7,756,424, “Optical CDMA communications system using OTDL device, have been used optical in fiber optic communications systems, to make more efficient use of the available bandwidth. Reed Muller codes, a subset of polar codes, can be used to achieve performance close to capacity limit predicted by the Shannon limit. Reed Muller decoders use linear error-correcting codes. Reed-Muller (RM) codes belong to the classes of locally testable codes, and locally decodable codes. RM codes are useful in the design of probabilistically checkable proofs in communication applications. Special cases of Reed-Muller codes include Hadamard codes, and Walsh-Hadamard codes.
It is known that RM codes have an elegant construction based on polynomials with specific structure. Higher order RM codes can be constructed recursively from lower order RM codes. This enables a decoding process that has complexity that is thousands of times smaller than other error correcting codes with similar performance, such as Reed Solomon codes.
Soft Decision Decoding
As known in the art, a hard-decision decoder decodes data that have a fixed set of discrete possible values, typically 0 or 1.
A soft-decision decoder decodes data that have been encoded with an error correcting code, and the data take on a range of continuous values from 0 to 1. The extra information indicates reliability (probability) of each input data point, and is used to form better estimates of the original data. Therefore, a soft-decision decoder typically performs better in the presence of corrupted data than hard-decision counterparts.
There are two types of soft decision decoders. First, a maximum likelihood (ML) decoder determines the probability that a specific codeword has been sent over a channel. Second, a maximum a posteriori (MAP) decoder determines the probability that information bit has been used to generate a codeword to be sent over a channel.